Arithmetic Structure in Dense Sets

稠密集中的算术结构

基本信息

项目摘要

This project focuses primarily on three different problems in number theory, combinatorics, and ergodic theory. This includes work in additive combinatorics concerning generalizations of Szemerédi's theorem on arithmetic progressions (sequences of numbers that are all equally spaced, like 4, 6, 8, and 10), which, informally, says that any sufficiently large collection of whole numbers contains a long arithmetic progression. It is a central problem in additive combinatorics to determine how large "sufficiently large" is. The investigator will study versions of this question involving more complicated patterns than arithmetic progressions, and then use the results and techniques developed to make progress on a related problem in ergodic theory. The investigator will also study the size and structure of integer distance sets, which are sets of points whose pairwise distances are all whole numbers. This award will support undergraduate summer research on representation theory and additive combinatorics, and also support the training of graduate students.More specifically, the investigator will build on her previous work on quantitative bounds for subsets of the integers lacking polynomial progressions of distinct degrees and for subsets of vector spaces over finite fields lacking a certain four-point configuration to tackle more general polynomial, multidimensional, and multidimensional polynomial configurations. The results for multidimensional polynomial configurations of distinct degree will then be used to make progress on the Furstenberg--Bergelson--Leibman conjecture in ergodic theory, which concerns the pointwise almost everywhere convergence of certain nonconventional ergodic averages. She will also investigate the size and structure of integer distance sets, in both the Euclidean plane and in higher dimensions, by encoding them as subsets of rational points on certain families of varieties and then studying these varieties. With her undergraduate students, the investigator will study the distribution of entries in the character tables of symmetric groups and some algorithmic problems in higher-order Fourier analysis.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
这个项目主要关注数论、组合学和遍历理论中的三个不同的问题。这包括关于Szemerédi关于算术级数(都是相等间隔的数字序列,如4、6、8和10)的推广的加法组合学方面的工作,该定理非正式地说,任何足够大的整数集合都包含一个长的算术级数。确定“足够大”有多大是加法组合学的核心问题。研究人员将研究这一问题的版本,涉及比算术级数更复杂的模式,然后使用所开发的结果和技术在遍历理论中的一个相关问题上取得进展。调查人员还将研究整数距离集的大小和结构,整数距离集是两两距离都是整数的点的集合。这一奖项将支持本科生夏季在表示理论和加性组合学方面的研究,也将支持研究生的培训。更具体地说,研究人员将在她之前工作的基础上,对缺乏不同次数多项式级数的整数子集和缺乏特定四点配置的有限域上的向量空间子集的量化界限进行研究,以解决更一般的多项式、多维和多维多项式配置。不同次数多项式构形的结果将被用于改进遍历理论中的Furstenberg-Berelson-Leibman猜想,该猜想涉及某些非常规遍历平均的逐点几乎处处收敛。她还将研究整数距离集的大小和结构,无论是在欧几里得平面上,还是在更高的维度上,通过将它们编码为某些变种上的有理点的子集,然后研究这些变种。这位研究人员将与她的本科生一起研究对称群特征标表中条目的分布以及高阶傅立叶分析中的一些算法问题。这一奖项反映了NSF的法定使命,并通过使用基金会的智力优势和更广泛的影响审查标准进行评估,被认为值得支持。

项目成果

期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)

数据更新时间:{{ journalArticles.updateTime }}

{{ item.title }}
{{ item.translation_title }}
  • DOI:
    {{ item.doi }}
  • 发表时间:
    {{ item.publish_year }}
  • 期刊:
  • 影响因子:
    {{ item.factor }}
  • 作者:
    {{ item.authors }}
  • 通讯作者:
    {{ item.author }}

数据更新时间:{{ journalArticles.updateTime }}

{{ item.title }}
  • 作者:
    {{ item.author }}

数据更新时间:{{ monograph.updateTime }}

{{ item.title }}
  • 作者:
    {{ item.author }}

数据更新时间:{{ sciAawards.updateTime }}

{{ item.title }}
  • 作者:
    {{ item.author }}

数据更新时间:{{ conferencePapers.updateTime }}

{{ item.title }}
  • 作者:
    {{ item.author }}

数据更新时间:{{ patent.updateTime }}

Sarah Peluse其他文献

On zeros of Eichler integrals
  • DOI:
    10.1007/s00013-013-0602-4
  • 发表时间:
    2014-01-12
  • 期刊:
  • 影响因子:
    0.500
  • 作者:
    Sarah Peluse
  • 通讯作者:
    Sarah Peluse
Cubic irrationals and periodicity via a family of multi-dimensional continued fraction algorithms
通过一系列多维连分数算法计算三次无理数和周期性
  • DOI:
    10.1007/s00605-014-0643-1
  • 发表时间:
    2012
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Krishna Dasaratha;Laure Flapan;T. Garrity;Chansoo Lee;Cornelia Mihaila;Nicholas Neumann;Sarah Peluse;Matthew Stoffregen
  • 通讯作者:
    Matthew Stoffregen
Quantitative bounds in the nonlinear Roth theorem
  • DOI:
    10.1007/s00222-024-01293-x
  • 发表时间:
    2024-10-07
  • 期刊:
  • 影响因子:
    3.600
  • 作者:
    Sarah Peluse;Sean Prendiville
  • 通讯作者:
    Sean Prendiville
Divisibility of character values of the symmetric group by prime powers
对称群的特征值可被质数幂整除
  • DOI:
  • 发表时间:
    2023
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Sarah Peluse;K. Soundararajan
  • 通讯作者:
    K. Soundararajan
Recent progress on bounds for sets with no three terms in arithmetic progression
算术级数中没有三项的集合的界限的最新进展
  • DOI:
  • 发表时间:
    2022
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Sarah Peluse
  • 通讯作者:
    Sarah Peluse

Sarah Peluse的其他文献

{{ item.title }}
{{ item.translation_title }}
  • DOI:
    {{ item.doi }}
  • 发表时间:
    {{ item.publish_year }}
  • 期刊:
  • 影响因子:
    {{ item.factor }}
  • 作者:
    {{ item.authors }}
  • 通讯作者:
    {{ item.author }}

{{ truncateString('Sarah Peluse', 18)}}的其他基金

Conference: Additive Combinatorics 2024
会议:加性组合学 2024
  • 批准号:
    2418414
  • 财政年份:
    2024
  • 资助金额:
    $ 35万
  • 项目类别:
    Standard Grant
PostDoctoral Research Fellowship
博士后研究奖学金
  • 批准号:
    1903038
  • 财政年份:
    2019
  • 资助金额:
    $ 35万
  • 项目类别:
    Fellowship Award

相似海外基金

Collaborative Research: Investigating Structure and Seismicity Within the Southern M9.2 1964 Great Alaska Earthquake Rupture Area Using a Dense Node Array
合作研究:使用密集节点阵列调查 1964 年 M9.2 大地震破裂区域南部的结构和地震活动
  • 批准号:
    2207441
  • 财政年份:
    2022
  • 资助金额:
    $ 35万
  • 项目类别:
    Standard Grant
Collaborative Research: Investigating Structure and Seismicity Within the Southern M9.2 1964 Great Alaska Earthquake Rupture Area Using a Dense Node Array
合作研究:使用密集节点阵列调查 1964 年 M9.2 大地震破裂区域南部的结构和地震活动
  • 批准号:
    2207389
  • 财政年份:
    2022
  • 资助金额:
    $ 35万
  • 项目类别:
    Standard Grant
Non uniformity in the PDL: structure and function of the dense collar
PDL 的不均匀性:致密环的结构和功能
  • 批准号:
    10491173
  • 财政年份:
    2021
  • 资助金额:
    $ 35万
  • 项目类别:
examination of the phase structure of high dense QCD matter within quantum molecular fluid dynamics
量子分子流体动力学中高密度 QCD 物质的相结构检查
  • 批准号:
    21K03577
  • 财政年份:
    2021
  • 资助金额:
    $ 35万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Non uniformity in the PDL: structure and function of the dense collar
PDL 的不均匀性:致密环的结构和功能
  • 批准号:
    10296840
  • 财政年份:
    2021
  • 资助金额:
    $ 35万
  • 项目类别:
Is tree having thick and dense crown vulnerable for global warming? Validation of a new hypothesis for inter-species variations in crown structure
树冠又厚又密的树木是否容易受到全球变暖的影响?
  • 批准号:
    21K19141
  • 财政年份:
    2021
  • 资助金额:
    $ 35万
  • 项目类别:
    Grant-in-Aid for Challenging Research (Exploratory)
Structure and motion of the inner core from dense arrays
密集阵列的内核结构和运动
  • 批准号:
    2041892
  • 财政年份:
    2021
  • 资助金额:
    $ 35万
  • 项目类别:
    Continuing Grant
Development of methods for analyzing anharmonic phonons and their application to structure searches in dense hydrogen and hydrides
非简谐声子分析方法的开发及其在稠密氢和氢化物结构搜索中的应用
  • 批准号:
    21K03437
  • 财政年份:
    2021
  • 资助金额:
    $ 35万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Non uniformity in the PDL: structure and function of the dense collar
PDL 的不均匀性:致密环的结构和功能
  • 批准号:
    10686415
  • 财政年份:
    2021
  • 资助金额:
    $ 35万
  • 项目类别:
Structure, Response, and Flow of Dense Granular Materials
致密颗粒材料的结构、响应和流动
  • 批准号:
    1809762
  • 财政年份:
    2018
  • 资助金额:
    $ 35万
  • 项目类别:
    Continuing Grant
{{ showInfoDetail.title }}

作者:{{ showInfoDetail.author }}

知道了